U sub help

1. The problem statement, all variables and given/known data
I'm trying to find the arc length of a curve over an interval and I've arrived at
[tex]\int[/tex] (y4 +2y2 +1)1/2 dy
and now I'm pretty sure i should use a u substitution in order to integrate.
I tried using u=y2 so du=2y dy so dy=du/2y
Then you have [tex]\int[/tex] (u2+2u+1)1/2 and eventually it boils down to [tex]\int[/tex] u+1 du which gives you u2/2 +u

But I think I forgot to incorporate the du/2y and I don't know if I can just change the answer to y2/2 + y.